Incremental Alignment Manifold Learning

• Published in: Journal of computer science and technology Vol. 26; no. 1; pp. 153 - 165
• Main Author: 韩志 孟德宇 徐宗本 古楠楠
• Format: Journal Article
• Language: English
• Published: Boston Springer US 2011; Springer Nature B.V
• Subjects: Algorithms; Alignment; Analysis; Artificial Intelligence; Computer Science; Data analysis; Data Structures and Information Theory; Datasets; Eigenvalues; Information Systems Applications (incl.Internet); Learning; Manifolds; Mathematical models; Minima; Neighborhoods; Nonlinear systems; Nonlinearity; Principal components analysis; Regular Paper; Representations; Science; Searching; Software Engineering; Studies; Teaching methods; Theory of Computation; 学习方法; 流形学习; 计算复杂性; 输入数据; 降维方法; 高维数据; out-of-sample issue; alignment; incremental learning; nonlinear dimensionality reduction; manifold learning
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/s11390-011-9422-9

A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire data.set. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects： high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.